1. Field of the Invention
The present invention relates to a boundary smoothing of a geometrical figure, and more particularly, to a boundary smoothing method of a geometrical figure using a terminal in which a smoothing operation on the boundary of the given geometrical figure is defined using sweep and unsweep operation in a process for processing the boundary of the geometrical figure using a CAD system or a graphic tool, thereby computing and processing the boundary at a high speed with good performance.
2. Description of the Related Art
Generally, smoothing operation is an essential geometrical factor in design and manufacturing process using a computer. For instance, smoothing of the boundary of geometrical figures is used to decorate fonts gracefully in industrial design appliances, to provide a special effect in movie industry appliances, and to design machinery and mold in the manufacturing industry appliances.
Conventionally, smoothing of the boundary of a geometrical figure needs to designate what degree of smoothing is applied to a region. Also, in order to computer the smoothing degree, it is needed to understand a differential property of a curve based on mathematical expression on the curve, and to apply a considerably complicated rule and computation. Especially, it is not easy to separately designate the smoothing application of the concave portion and the convex portion. In addition, a computation using differential property of a curve has a considerably large computational amount compared with the cross computation between straight lines, and is naturally sensitive to a numerical error.
Korean Patent laid open number 2001-058236 entitled “Offset curve computational method of plane object using sweep/unsweep” discloses a method for computing an offset curve of a boundary of a plane object by sequentially applying sweep/unsweep operations based on the most basic plane geometry Boolean set operation in geometry operation.
In the prior Korean Patent, the method for computing the offset curve of the plane object using sweep/unsweep includes: a first step of computing sweep by setting a boundary line P(t) of an object O, and then setting a circle A having an offset radius d; and a second step of setting an external boundary line of S obtained by the first step as an external offset curve of the object O, and an internal boundary line of S as an internal offset curve of the object O. This method is operated only based on the Boolean set operation.
Korean Patent Application number 2000-80906 entitled “Method for Extracting General Sweep Boundary Line Using Sweep-Envelop and Line Sweep Operation” is a method for extracting a boundary line of a general sweep, and it is to express a region where an object moving along a given path has passed.
The prior Korean Patent application is to extract a boundary line of a complicated general sweep by a simple approximation of the sweep-envelop instead of using a mathematically complicated differential property of the boundary line, but it does not provide any method for the sweep-unsweep.
Meanwhile, the sweep means a region where an object moved along a specific path has swept, and it is a very difficult item to extract the boundary line expressing the region. As means to solve this problem, there is known a method using the boundary line of an object and the algebraic property. However, since this method has a difficulty in inducing an equation and also has many cases that are complex and unstable in numerical computation, it can be applied to a simple problem alone.
The unsweep means a region where an object moved along a specific path sweeps always. A computational method of the unsweep is more difficult than that of the sweep, and is not well known.